Maximum stress of stiff elastic plate in uniform flow and due to jet impact

The liquid jet impact onto a clamped elastic plate is investigated. The two-dimensional jet of constant thickness and with flat vertical front is initially advancing towards the elastic plate along a flat, rigid, and horizontal plane at a constant uniform speed. The elastic plate of variable thickness is mounted perpendicular to the rigid plane. The maximum stress during the early impact stage is estimated for a given retardation time and a given relaxation time of the plate material. The stresses during the initial impact stage are compared with the static stresses in the plate placed in an equivalent uniform flow. It is shown that the static stresses are always smaller than the bending stresses during the early stage of impact for a given speed and thickness of the jet. This implies that if the stresses in the plate are smaller than the yield stress of the plate material with no plastic deformations in the plate occurring during the unsteady impact stage, then the plate behaves elastically after the impact and plastic deformations are not achieved. Approaching the plastic deformations is treated here as a damage to the plate. The maximum stress increases with an increase in jet thickness. A critical value of the jet velocity, below which the plate is not damaged by the jet impact, is obtained for given characteristics of the plate

On the use of euler and crank-nicolson time-stepping schemes for seakeeping simulations in openfoam

The open-source CFD software package OpenFOAM has reached a maturity level such that it is possible to perform seakeeping simulations using the included VOF-based free- surface URANS (Unsteady-Reynolds-Averaged Navier-Stokes) solver (a.k.a interDyMFoam). This paper describes results of seakeeping tests and the experiences obtained while selecting an appropriate combination of spatial and temporal schemes for wave and seakeeping simula- tions in a regular head sea condition. Particular attention has been paid to the accuracy level and the convergence rate of temporal schemes Euler and CrankNicolson since an accurate tem- poral discretization is known to be very important for wave propagations. Here the numerical results confirm the need for at least a 2nd-order temporal scheme. To improve the stability and the robustness of the existing CrankNicolson scheme we customized the code and performed a numerical experiment on the modified CrankNicolson scheme where the off-centering parameter co is non-uniformly distributed in the domain. The results show that when using a simple distri- bution of the co parameter the stability of the CrankNicolson scheme can be restored without having to degrade significantly the numerical order of the scheme. This new approach allows stable simulations to be performed where the incident wave field is propagated more acceptably with a very small decay and, at the same time, keeps the time step large enough to allow the simulations to finish at a reasonable CPU time

The vertical mode method in the problems of flexural-gravity waves diffracted by a vertical cylinder

The linear three-dimensional problem of ice loads acting on a vertical circular cylinder frozen in an ice cover of infinite extent is studied. The loads are caused by an uni-directional hydroelastic wave propagating in the ice cover towards the cylinder mounted to the see bottom in water of constant depth. There are no open water surfaces in this problem. The deflection of the ice cover is described by the Bernoulli-Euler equation of a thin elastic plate of constant thickness. At the contact line between the ice cover and the surface of the cylinder, some edge conditions are imposed. In this study, the edge of the ice plate is either clamped to the cylinder or has no contact with the cylinder surface, with the plate edge being free of stresses and shear forces. The water is of finite constant depth, inviscid and incompressible. The problem is solved by both the vertical mode method and using the Weber integral transform in the radial coordinate. Each vertical mode corresponds to a root of the dispersion relation for flexural-gravity waves. It is proved that these two solutions are identical for the clamped edge conditions. This result is non-trivial because the vertical modes are non-orthogonal in a standard sense, they are linearly dependent, the roots of the dispersion relation can be double and even triple, and the set of the modes could be incomplete. A general solution of the wave-cylinder interaction problem is derived by the method of vertical modes and applied to different edge conditions on the contact line. There are three conditions of solvability in this problem. It is shown that these conditions are satisfied for any parameters of the problem

Global hydroelastic model for springing and whipping based on a free-surface CFD code (OpenFOAM)

The theoretical background and a numerical solution procedure for a time domain hydroelastic code are presented in this paper. The code combines a VOF-based free surface flow solver with a flexible body motion solver where the body linear elastic deformation is described by a modal superposition of dry mode shapes expressed in a local floating frame of reference. These mode shapes can be obtained from any finite element code. The floating frame undergoes a pseudo rigid-body motion which allows for a large rigid body translation and rotation and fully preserves the coupling with the local structural deformation. The formulation relies on the ability of the flow solver to provide the total fluid action on the body including e.g. the viscous forces, hydrostatic and hydrodynamic forces, slamming forces and the fluid damping. A numerical simulation of a flexible barge is provided and compared to experiments to show that the VOF-based flow solver has this ability and the code has the potential to predict the global hydroelastic responses accurately

Rational Assessment of Fluid Impact Loads

The safe operation of ships is a high priority task in order to protect the ship, the personnel, the cargo and the wider environment. A methodology for the rational and reliable assessment of the structural integrity and thus safety of ships and their cargos at sea has been developed. Central to this methodology is a set of mathematical models, the conditions of their use, and the links between them, which were designed to improve the predictions of wave impact loads acting on ships. The models, together with the methodology of their use, were utilised by the ship certification industry bringing benefits through recognised quality assurance systems and certification

Hydro-structural issues in the design of ultra large container ships

ABSTRACTThe structural design of the ships includes two main issues which should be checked carefully, namely the extreme structural response (yielding & buckling) and the fatigue structural response. Even if the corresponding failure modes are fundamentally different, the overall methodologies for their evaluation have many common points. Both issues require application of two main steps: deterministic calculations of hydro-structure interactions for given operating conditions on one side and the statistical post-processing in order to take into account the lifetime operational profile, on the other side. In the case of ultra large ships such as the container ships and in addition to the classical quasi-static type of structural responses the hydroelastic structural response becomes important. This is due to several reasons among which the following are the most important: the increase of the flexibility due to their large dimensions (Lpp close to 400 m) which leads to the lower structural natural frequencies, very large operational speed (20 knots) and large bow flare (increased slamming loads). The correct modeling of the hydroelastic ship structural response, and its inclusion into the overall design procedure, is significantly more complex than the evaluation of the quasi static structural response. The present paper gives an overview of the different tools and methods which are used in nowadays practice

Solution and domain decomposition model for marine hydrodynamics: rans and potential flow coupling

This paper presents a CFD decomposition model for free surface, viscous, in- compressible flows related to marine hydrodynamics. The solution decomposition is based on Spectral Wave Explicit Navier Stokes Equations (SWENSE), where the primitive vari- ables are written as the combination of incident and diffracted fields. This allows efficient coupling of the discretised Navier–Stokes free surface flow equations with arbitrary poten- tial flow theories. The domain decomposition is achieved with implicit relaxation zones in order to prevent undesirable wave reflection in unbounded domains. Interface captur- ing is obtained with implicitly redistanced Level Set (LS) method derived from Phase Field equation. This approach removes the need to redistance the LS field using conven- tional redistancing procedures and reduces mass conservation issues fundamental to the LS method. The numerical model is based on a polyhedral, second-order accurate, col- located finite volume method (FVM). The coupling of primitive variables is obtained via segregated solution algorithm based on SIMPLE and PISO. The model is implemented in OpenFOAM. The verification of the model is performed by a number of two–dimensional (2–D) test cases. The reflection analysis is carried out by changing the relaxation zone length. Mass conservation and preservation of the signed distance LS function is demon- strated with a simulation lasting 50 incident wave periods. A long domain simulation is also carried out to show that the damping of the wave does not occur. Finally, a wave steepness study has been carried out by changing wave height while the wave period was kept fixed. Three–dimensional (3–D) test cases regarding higher order forces on circular cylinder have also been carried out. However, the results will be presented in future work

Étude hydroélastique globale du LNG 175k

L'étude de la réponse hydroélastique d'un corps nécessite la prise en compte de l'effet de la houle et celui des carènes liquides à bord (problème de ballottement dans les cuves ou sloshing), et de coupler ces deux phénomènes afin d'analyser le comportement structurel global du corps. La formulation du problème de sloshing est souvent basée sur des modèles simplifiés qui peuvent être justifiés par le fait que la masse du liquide dans les cuves est négligeable par rapport à la masse totale du corps. Néanmoins, plusieurs types de navire échappent à cette hypothèse comme les navires-citernes et les méthaniers; où il faudra considérer des modèles encore plus réalistes. Jusqu'à présent, peu de travaux ont traité cette problématique de couplage avec la prise en compte du comportement élastique des cuves [Kim K.T. et al. 2015]. Au cours des dernières années, nous avons mis en place un modèle hydroélastique basé sur le couplage de la théorie potentielle 3D (le logiciel Bureau Veritas Hydrostar) et la méthode des éléments finis 3D (Nastran) afin de prendre en compte à la fois le problème extérieur (houle) et intérieur (sloshing). A ce stade, seule l'approche potentielle linéaire est considérée et le problème est formulé dans le domaine fréquentiel. Ce modèle a été validé grâce à des comparaisons avec des cas test académiques (solutions semi-analytiques) puis utilisé pour l'étude de la réponse hydroélastique d'un méthanier. Dans un premier temps, les fréquences propres et les déformées modales seront déterminées ; ensuite la réponse linéaire du navire sera analysée afin d'évaluer le degré d'influence des carènes liquides sur la réponse hydroélastique globale et locale. D'autres modèles simplifiés seront également présentés (pour le problème intérieur) puis comparés au modèle complet proposé

Étude hydroélastique globale du LNG 175k

L'étude de la réponse hydroélastique d'un corps nécessite la prise en compte de l'effet de la houle et celui des carènes liquides à bord (problème de ballottement dans les cuves ou sloshing), et de coupler ces deux phénomènes afin d'analyser le comportement structurel global du corps. La formulation du problème de sloshing est souvent basée sur des modèles simplifiés qui peuvent être justifiés par le fait que la masse du liquide dans les cuves est négligeable par rapport à la masse totale du corps. Néanmoins, plusieurs types de navire échappent à cette hypothèse comme les navires-citernes et les méthaniers; où il faudra considérer des modèles encore plus réalistes. Jusqu'à présent, peu de travaux ont traité cette problématique de couplage avec la prise en compte du comportement élastique des cuves [Kim K.T. et al. 2015]. Au cours des dernières années, nous avons mis en place un modèle hydroélastique basé sur le couplage de la théorie potentielle 3D (le logiciel Bureau Veritas Hydrostar) et la méthode des éléments finis 3D (Nastran) afin de prendre en compte à la fois le problème extérieur (houle) et intérieur (sloshing). A ce stade, seule l'approche potentielle linéaire est considérée et le problème est formulé dans le domaine fréquentiel. Ce modèle a été validé grâce à des comparaisons avec des cas test académiques (solutions semi-analytiques) puis utilisé pour l'étude de la réponse hydroélastique d'un méthanier. Dans un premier temps, les fréquences propres et les déformées modales seront déterminées ; ensuite la réponse linéaire du navire sera analysée afin d'évaluer le degré d'influence des carènes liquides sur la réponse hydroélastique globale et locale. D'autres modèles simplifiés seront également présentés (pour le problème intérieur) puis comparés au modèle complet proposé